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Responsible: Ben Goertzel
Traditional inference systems waste effort oscillating between forward chaining (from facts toward goals) and backward chaining (from goals toward facts). Geodesic inference eliminates this inefficiency by maintaining both directions simultaneously and choosing steps that advance both — following minimum-effort paths through inference space.
Core Concept
Geodesic control implements inference as navigation along shortest paths through information space, where "shortest" means minimum representational effort as defined by weakness theory. At each step, the system maintains two factors:
Forward factor (f): reachability from current evidence — what can we derive from what we know?
Backward factor (g): usefulness toward current goals — what would help us reach our objectives?
The control rule is straightforward: choose actions that maximize the change in log(f × g) per unit cost, while maintaining approximately constant effort per step. This f·g product structure appears throughout PRIMUS — in inference, evolutionary search, transfer learning, Schrödinger bridge interpolation, and even motivational decisions.
Mathematical Foundation
The approach is grounded in Schrödinger bridge geometry, defining an action functional that combines transport effort with prior regularization. The optimal solution has an elegant property: at each point, the probability density is proportional to the product of forward and backward factors.
In practice, the factors are approximated through:
Factor-graph messages for logical inference (PLN)
Monte Carlo estimates for meet probabilities
Amortized neural predictors for complex domains
Evidence Conservation
Geodesic control enforces a critical safety property: conservation of evidence. Just as physical systems conserve energy, the inference system ensures that evidence neither spontaneously appears nor disappears — preventing both hallucination and information loss.
This emerges from a quantale-valued "generalized energy" that acts as a Noether invariant. Implementation uses local evidence capsules (similar to CRDTs), overlap-safe merge operations, and content-addressed messages in the scheduler.
Role in PRIMUS
Geodesic control is one of two architecture-wide formal controls (alongside weakness theory). It provides the selection rule for:
PLN inference step selection
MOSES/GEO-EVO evolutionary search direction
Planning and action selection
Self-modification proposal evaluation
Schrödinger bridge curriculum design
The approach is particularly elegant within PLN, where it unifies forward and backward chaining into a single bidirectional process guided by principled cost metrics.
Key References
Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.2: Geodesic Inference and Control
Traditional inference systems waste effort oscillating between forward chaining (from facts toward goals) and backward chaining (from goals toward facts). Geodesic inference eliminates this inefficiency by maintaining both directions simultaneously and choosing steps that advance both — following minimum-effort paths through inference space.
Core Concept
Geodesic control implements inference as navigation along shortest paths through information space, where "shortest" means minimum representational effort as defined by weakness theory. At each step, the system maintains two factors:
Forward factor (f): reachability from current evidence — what can we derive from what we know?
Backward factor (g): usefulness toward current goals — what would help us reach our objectives?
The control rule is straightforward: choose actions that maximize the change in log(f × g) per unit cost, while maintaining approximately constant effort per step. This f·g product structure appears throughout PRIMUS — in inference, evolutionary search, transfer learning, Schrödinger bridge interpolation, and even motivational decisions.
Mathematical Foundation
The approach is grounded in Schrödinger bridge geometry, defining an action functional that combines transport effort with prior regularization. The optimal solution has an elegant property: at each point, the probability density is proportional to the product of forward and backward factors.
In practice, the factors are approximated through:
Factor-graph messages for logical inference (PLN)
Monte Carlo estimates for meet probabilities
Amortized neural predictors for complex domains
Evidence Conservation
Geodesic control enforces a critical safety property: conservation of evidence. Just as physical systems conserve energy, the inference system ensures that evidence neither spontaneously appears nor disappears — preventing both hallucination and information loss.
This emerges from a quantale-valued "generalized energy" that acts as a Noether invariant. Implementation uses local evidence capsules (similar to CRDTs), overlap-safe merge operations, and content-addressed messages in the scheduler.
Role in PRIMUS
Geodesic control is one of two architecture-wide formal controls (alongside weakness theory). It provides the selection rule for:
PLN inference step selection
MOSES/GEO-EVO evolutionary search direction
Planning and action selection
Self-modification proposal evaluation
Schrödinger bridge curriculum design
The approach is particularly elegant within PLN, where it unifies forward and backward chaining into a single bidirectional process guided by principled cost metrics.
Key References
Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.2: Geodesic Inference and Control